兩圓O1,O2相交於AB兩點
公切線L1交兩圓於C,D 2點
延長AB交L1於E
證明:CE=DE
siuhochung 寫到:補圖及原因
angle CEA=angle BEC (common angle)
angle ECA=angle EBC (angle in alt. seg.)
angle CAE=180-angle CEA -angleECA
=180-angle BEC-angle EBC
=angle BCE
CEA~BEC (AAA)
CE^2 = EA*BE (corr. sides, ~tri.)
angle DEA=angle BED (common angle)
angle EDA=angle EBD (angle in alt. seg.)
angle DAE=180-angle DEA -angleEDA
=180-angle BED-angle EBD
=angle BDE
DEA~BED (AAA)
DE^2 = EA*BE (corr. sides, ~tri.)
CE^2=DE^2
CE=DE